Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set - Page 409: 66

$27y^{5}$

Using the laws of exponents, the given expression, $ (3y^4)^3y^{-7} ,$ simplifies to \begin{array}{l}\require{cancel} 3^{1(3)}y^{4(3)}y^{-7} \\\\= 3^{3}y^{12}y^{-7} \\\\= 27y^{12+(-7)} \\\\= 27y^{12-7} \\\\= 27y^{5} .\end{array}